3hr0n1um
Answered

Westonci.ca is the ultimate Q&A platform, offering detailed and reliable answers from a knowledgeable community. Join our platform to connect with experts ready to provide precise answers to your questions in different areas. Join our Q&A platform to connect with experts dedicated to providing accurate answers to your questions in various fields.

if(√14/√7-2)-(√14/√7+2)=a√7+b√2 find the values of a and b where a and b are rational numbers​

Sagot :

mhanifa

Answer:

  • a = 4/3 and b = 0

============================

Given expression:

[tex]\dfrac{\sqrt{14} }{\sqrt{7}-2} -\dfrac{\sqrt{14} }{\sqrt{7}+2}[/tex]

Simplify it in steps:

Step 1

Bring both fractions into common denominator:

[tex]\dfrac{\sqrt{14} (\sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} - \dfrac{\sqrt{14} (\sqrt{7}-2)}{(\sqrt{7}-2)(\sqrt{7}+2)}[/tex]

Step 2

Simplify:

[tex]\dfrac{\sqrt{14} ((\sqrt{7}+2) - (\sqrt{7}-2))}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{\sqrt{14} (\sqrt{7}+2 - \sqrt{7}+2)}{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{4\sqrt{14} }{(\sqrt{7}-2)(\sqrt{7}+2)} =[/tex]

[tex]\dfrac{4\sqrt{14} }{(\sqrt{7})^2-2^2} =[/tex]

[tex]\dfrac{4\sqrt{14} }{7-4} =[/tex]

[tex]\dfrac{4}{3} \sqrt{14} }[/tex]

Step 3

Compare the result with given expression to get:

  • a = 4/3 and b = 0

Thank you for trusting us with your questions. We're here to help you find accurate answers quickly and efficiently. We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Discover more at Westonci.ca. Return for the latest expert answers and updates on various topics.